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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
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15 include "static_2/relocation/lifts_teqx.ma".
16 include "static_2/static/rex_drops.ma".
17 include "static_2/static/reqx.ma".
19 (* SORT-IRRELEVANT EQUIVALENCE FOR LOCAL ENVIRONMENTS ON REFERRED ENTRIES ***)
21 (* Properties with generic slicing for local environments *******************)
23 lemma reqx_lifts_sn: f_dedropable_sn cdeq.
24 /3 width=5 by rex_liftable_dedropable_sn, teqx_lifts_sn/ qed-.
26 (* Inversion lemmas with generic slicing for local environments *************)
28 lemma reqx_inv_lifts_sn: f_dropable_sn cdeq.
29 /2 width=5 by rex_dropable_sn/ qed-.
31 lemma reqx_inv_lifts_dx: f_dropable_dx cdeq.
32 /2 width=5 by rex_dropable_dx/ qed-.
34 lemma reqx_inv_lifts_bi: โL1,L2,U. L1 โ[U] L2 โ โb,f. ๐โชfโซ โ
35 โK1,K2. โฉ*[b,f] L1 โ K1 โ โฉ*[b,f] L2 โ K2 โ
36 โT. โง*[f] T โ U โ K1 โ[T] K2.
37 /2 width=10 by rex_inv_lifts_bi/ qed-.
39 lemma reqx_inv_lref_pair_sn: โL1,L2,i. L1 โ[#i] L2 โ โI,K1,V1. โฉ[i] L1 โ K1.โ[I]V1 โ
40 โโK2,V2. โฉ[i] L2 โ K2.โ[I]V2 & K1 โ[V1] K2 & V1 โ V2.
41 /2 width=3 by rex_inv_lref_pair_sn/ qed-.
43 lemma reqx_inv_lref_pair_dx: โL1,L2,i. L1 โ[#i] L2 โ โI,K2,V2. โฉ[i] L2 โ K2.โ[I]V2 โ
44 โโK1,V1. โฉ[i] L1 โ K1.โ[I]V1 & K1 โ[V1] K2 & V1 โ V2.
45 /2 width=3 by rex_inv_lref_pair_dx/ qed-.
47 lemma reqx_inv_lref_pair_bi (L1) (L2) (i):
49 โI1,K1,V1. โฉ[i] L1 โ K1.โ[I1]V1 โ
50 โI2,K2,V2. โฉ[i] L2 โ K2.โ[I2]V2 โ
51 โงโง K1 โ[V1] K2 & V1 โ V2 & I1 = I2.
52 /2 width=6 by rex_inv_lref_pair_bi/ qed-.